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Author Biess, A.; Liebermann, D.G.; Flash, T.
Title A computational model for redundant human three-dimensional pointing movements: integration of independent spatial and temporal motor plans simplifies movement dynamics Type Journal Article
Year 2007 Publication The Journal of Neuroscience : the Official Journal of the Society for Neuroscience Abbreviated Journal J Neurosci
Volume 27 Issue (up) 48 Pages 13045-13064
Keywords Analysis of Variance; Arm/physiology; Biomechanics; *Computer Simulation; Humans; *Models, Biological; Movement/*physiology; *Nonlinear Dynamics; Posture/physiology; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Time Factors; Torque
Abstract Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties (path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed-dependent torques vanishes. The temporal properties of the movement (speed) are determined in task space by minimizing the squared jerk along the selected end-effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques.
Address Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel. armin.biess@weizmann.ac.il
Corporate Author Thesis
Publisher Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0270-6474 ISBN Medium
Area Expedition Conference
Notes PMID:18045899 Approved no
Call Number Serial 35
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Author Liebermann, D.G.; Krasovsky, T.; Berman, S.
Title Planning maximally smooth hand movements constrained to nonplanar workspaces Type Journal Article
Year 2008 Publication Journal of Motor Behavior Abbreviated Journal J Mot Behav
Volume 40 Issue (up) 6 Pages 516-531
Keywords Adaptation, Physiological; Adult; Algorithms; Female; Hand/*physiology; Humans; *Intention; Kinesthesis/*physiology; Male; Models, Statistical; Movement/*physiology; Psychomotor Performance/*physiology; Reference Values; Writing
Abstract The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.
Address Department of Physical Therapy, The Stanley Steyer School of Health Professions, Sackler Faculty of Medicine, Tel Aviv University, Israel. dlieberm@post.tau.ac.il
Corporate Author Thesis
Publisher Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0022-2895 ISBN Medium
Area Expedition Conference
Notes PMID:18980905 Approved no
Call Number Serial 33
Permanent link to this record